Question: Simplify the following expression: $\dfrac{20x^4}{50x^2}$ You can assume $x \neq 0$.
$ \dfrac{20x^4}{50x^2} = \dfrac{20}{50} \cdot \dfrac{x^4}{x^2} $ To simplify $\frac{20}{50}$ , find the greatest common factor (GCD) of $20$ and $50$ $20 = 2 \cdot 2 \cdot 5$ $50 = 2 \cdot 5 \cdot 5$ $ \mbox{GCD}(20, 50) = 2 \cdot 5 = 10 $ $ \dfrac{20}{50} \cdot \dfrac{x^4}{x^2} = \dfrac{10 \cdot 2}{10 \cdot 5} \cdot \dfrac{x^4}{x^2} $ $\phantom{ \dfrac{20}{50} \cdot \dfrac{4}{2}} = \dfrac{2}{5} \cdot \dfrac{x^4}{x^2} $ $ \dfrac{x^4}{x^2} = \dfrac{x \cdot x \cdot x \cdot x}{x \cdot x} = x^2 $ $ \dfrac{2}{5} \cdot x^2 = \dfrac{2x^2}{5} $